Question

There are 40 students in a chemistry class and 60 students in a physics class. Find the number of students which are either in physics class or chemistry class in the following case:

The two classes meet at different hours and 20 students are enrolled in both the subjects

Answer 1

Let A be the set of students in chemistry class and B be the set of students in physics class. It is given that $n\left(A\right)=40$ and $n\left(B\right)=60$.
If two classes meet at different timings then there can be some student sitting in both the classes.
Therefore, $n(A\cap B)=20$
$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$
$=40+60-20=80$.